Spectral uniqueness of radial semiclassical Schrodinger operators

TL;DR

This paper demonstrates that the spectrum of an n-dimensional semiclassical radial Schrödinger operator uniquely determines the potential within a broad class, using semiclassical trace invariants and isoperimetric inequality.

Contribution

It introduces a novel spectral uniqueness result for radial semiclassical Schrödinger operators without symmetry or analyticity assumptions.

Findings

Spectrum determines the potential in a broad class of cases

Utilizes semiclassical trace invariants for analysis

Employs isoperimetric inequality in proof

Abstract

We prove that the spectrum of an n-dimensional semiclassical radial Schr\"odinger operator determines the potential within a large class of potentials for which we assume no symmetry or analyticity. Our proof is based on the first two semiclassical trace invariants and on the isoperimetric inequality.